论文标题
具有随机力和应力的结构优化算法
A structural optimization algorithm with stochastic forces and stresses
论文作者
论文摘要
我们提出了一种算法，以进行优化，其中梯度包含随机噪声。例如，当力和应力的计算依赖于涉及蒙特卡洛采样的方法（例如量子蒙特卡洛或神经网络状态）或在具有内在噪声的量子设备上执行的方法时，就会在结构优化中产生。我们提出的算法基于两种关键成分的组合：从最陡峭的下降方法得出的更新规则，以及针对目标统计误差和阶梯尺寸的阶段调度，并进行平均位置。我们将其与常用算法（包括一些最新的机器学习优化方法）进行了比较，并表明该算法在现实条件下始终如一，有效地执行。采用该算法，我们使用辅助场量子蒙特卡洛（Monte Carlo）带有Planewaves和pseudoptientss，使用从头开始多体计算实现固体中的全能优化。在混合的几何形状和晶格放松模拟中发现了SI中的新亚稳态结构。除了材料中的结构优化外，我们的算法在需要使用噪声梯度优化的各个领域的其他问题中也可能有用。
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such as quantum Monte Carlo or neural network states, or are performed on quantum devices which have intrinsic noise. Our proposed algorithm is based on the combination of two key ingredients: an update rule derived from the steepest descent method, and a staged scheduling of the targeted statistical error and step-size, with position averaging. We compare it with commonly applied algorithms, including some of the latest machine learning optimization methods, and show that the algorithm consistently performs efficiently and robustly under realistic conditions. Applying this algorithm, we achieve full-degree optimizations in solids using ab initio many-body computations, by auxiliary-field quantum Monte Carlo with planewaves and pseudopotentials. A new metastable structure in Si was discovered in a mixed geometry and lattice relaxing simulation. In addition to structural optimization in materials, our algorithm can potentially be useful in other problems in various fields where optimization with noisy gradients is needed.
